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Ballistic transport under Quantum Hall effect conditions

Ballistic transport under Quantum Hall effect conditions

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Ballistic transport under Quantum Hall effect conditions

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  1. Ballistic transport under Quantum Hall effect conditions S.Nazin, V.Shikin, ISSP RAS

  2. Outline • 1. 1-D ballistic conductance definition • 2.Hall-effect, Quantum Hall-effect (QHE) definitions • 3. Edge (ballistic) scenario for QHE realization (Halperin, 1982; Buttiker, 1986) • 4. Technical service for Halperin-Buttiker scenario . • 5. Resume.

  3. 1-D channel ballistic coductance.

  4. Narrow 1-D channel definition

  5. Conductance G(V)

  6. 2D Hall-bar setup

  7. Shub-de-Haas oscillationsand the Hall resistance for 1-D ballistic channel.

  8. Conventional skipping states in magnetic field

  9. Data: Phys.Rev B 38 , 3625

  10. B.I.Shklovskii et al., Phys. Rev. B46 (1992) p.4026

  11. 1-D channel electrostatics

  12. The corresponding density profile n(x) and the $x_l$ - point positions definition

  13. H=1.02………………….H=1.05

  14. Resume: • 1. Self consistent description of 1-D channel ballistic conductance under QHE conditions is presented . • 2. Benefice to B.Shklovski idea • 2. In general the activity around MES (magnetic edge states) is not so routine.

  15. External potential, the profile n(x) of electron density, position of static skin-layer and its relative scale

  16. QHE without edge states

  17. H =0.6

  18. Saddle point influence